When the Greeks were settling around the Mediterranean they founded many 'New Cities', (Neapolis). One remained a 'new city' for long enough for the name to evolve to Naples.
The Phoenicians did the same, in their language 'New City' was Qart Hadasht, we now call it Carthage. One of the Carthages in what is now Spain was conquered by Rome and to differentiate it from the Capital of the Carthaginians they called it Carthago Nova, essentially New New City.
Tbf a lot of the ‘new[city]’ was given their names by the British empire expanding their land. Just look at Australian state names.. The Americans doing this in more recent times are simply following suit.
Poland, Indiana
Poland, Maine
Poland, Chautauqua County, New York
Poland, Herkimer County, New York
Poland, Ohio
Poland Township, Mahoning County, Ohio
Poland, Wisconsin
For example Manna-hatta was renamed by Europeans (specifically the Dutch) New Amsterdam and later renamed again by Europeans (this time the English) as New York.
By the time there were officially "Americans" (i.e. after the Independence of the United States) the deed was already done.
Wait until you hear about Latin American colonizers taking inspiration in the cities of "Granada", "Córdoba" and "Santiago" to name their cities "Granada", "Córdoba" and "Santiago". At least Venezuela changed a couple letters from Venezia.